Carathéodory's theorem is a theorem in complex analysis, named after Constantin Carathéodory, which extends the Riemann mapping theorem. The theorem,...

mathematics, Carathéodory's theorem may refer to one of a number of results of Constantin Carathéodory: Carathéodory's theorem (conformal mapping), about the...

Riemann mapping theorem Schwarz–Christoffel mapping – a conformal transformation of the upper half-plane onto the interior of a simple polygon. Conformal radius...

Biholomorphic map Carathéodory's theorem – A conformal map extends continuously to the boundary Penrose diagram Schwarz–Christoffel mapping – a conformal transformation...

known as Carathéodory's method of equivalent variational problems or the royal road to the calculus of variations. A key advantage of Carathéodory's work...

manifold) Arakelyan's theorem (complex analysis) Area theorem (conformal mapping) (complex analysis) Arithmetic Riemann–Roch theorem (algebraic geometry)...

Riemann mapping theorem Carathéodory's theorem (conformal mapping) Riemann–Roch theorem Amplitwist Antiderivative (complex analysis) Bôcher's theorem Cayley...

Jordan-Schoenflies theorem for continuous curves can be proved using Carathéodory's theorem on conformal mapping. It states that the Riemann mapping between the...

analytic functions Montel's theorem Poincaré metric Schwarz lemma Riemann mapping theorem Carathéodory's theorem (conformal mapping) Böttcher's equation Orbit...

conformal structures. Indeed, conformal structures are the same as complex structures in two (real) dimensions. Moreover, the Uniformisation Theorem also...

in one complex dimension (such as conformality) do not carry over. The Riemann mapping theorem about the conformal relationship of certain domains in...

derivative there. By the Carathéodory kernel theorem fn(z) converges uniformly on compacta in Ω to z. In fact Carathéodory's theorem implies that the inverse...

group but also determines the Riemann surface up to conformal equivalence. By the uniformization theorem, every compact Riemann surface has simply connected...

actively studied in the theory of circle packing. Carathéodory's theorem (conformal mapping) Jordan curve theorem Schoenflies problem Kodaira 2007, pp. 257,...

expands continuously in the sense of Carathéodory to the whole plane leads to a one parameter family of conformal mappings, called a Loewner chain, as well...

important papers, one with Carathéodory on entire functions in 1907 and another major work with Frigyes Riesz in 1922 on conformal mappings (specifically, a short...

derivative § Conformal mapping of circular arc polygons for more details. L. P. Lee used Schwarz triangle functions to derive conformal map projections...

and only if they are conformal to one another. For this reason, the study of Riemann surfaces is identical to the study of conformal classes of Riemannian...

of level curves of the conformal mapping of simply connected domains to the interior of a circle: A generalization of a theorem of Eduard Study"). This...

left-continuous, w([s,t)) = g(t) − g(s) and w({b}) = 0). By Carathéodory's extension theorem, there is a unique Borel measure μg on [a, b] which agrees...

the circle is a quasicircle. Conversely, using the Riemann mapping theorem, the conformal maps f and g uniformizing the outside of a quasicircle give...

point in the prime ends of B. Carathéodory's principal theorem on the correspondence between boundaries under conformal mappings can be expressed as follows:...

estimating the integral of powers of the moduli of the derivative of conformal maps into the open unit disk, on certain subsets of C {\displaystyle \mathbb...

Interscience Publishers Inc., 1968. Courant, R.: Dirichlet's principle, conformal mapping and minimal surfaces. Interscience, 1950. Dacorogna, Bernard: "Introduction"...

4310/jdg/1214446319 Courant, Richard (1950), Dirichlet's Principle, Conformal Mapping and Minimal Surfaces, John Wiley & Sons, ISBN 978-0-486-44552-6 Darboux...

connections and conformal connections. Kobayashi (2005), sections IV.1 and VII.2. Kobayashi (2005), Proposition IV.1.6. Kobayashi (1998), Theorem 3.6.3. Kobayashi...

for twice continuously differentiable u {\displaystyle u} (mean value theorem) but may be proved in a distributional sense as well. We define a new operator...

( Ω ) {\displaystyle \Pi _{D}~:~X_{D,0}\to L^{2}(\Omega )} is a linear mapping that reconstructs, from an element of X D , 0 {\displaystyle X_{D,0}} ...

"Discontinuous Groups and Automorphic Functions", being one example. Carathéodory's elementary treatment in his 1950 textbook Funktiontheorie, translated...

portrait Periodic points of complex quadratic mappings Prouhet-Thue-Morse constant Carathéodory's theorem Field lines of Julia sets J. Kiwi : Rational...